Which are the best lens you can use with nikon d3100?

I want to now what lens should i use with nikon3100 dslr camera for shooting a movie of a swimming competition?

Nikon AF-S 70-200mm f/2.8 VRII… After you get over sticker shock:

Sigma 70-200mm f/2.8… Is an aftermarket lens at about half the cost.

Each of these lenses are telephoto lenses, and have fast optics, which are necessary for action photos or when the lighting is not ideal.

While you can buy a consumer-grade 55-300 or 70-300 for a lot less than the above two, these are optically slower, and will let only about 25% of the light in at the extreme telephoto end. This lens may work OK for you in daylight conditions; inside not so much.

Before I bought my pro grade 80-200mm f/2.8, I had a 70-300mm lens and was able to take photos of hockey games. I had to increase the ISO to 6400 to get a shot, but it added a lot of noise. I was able to get rid of most of the noise with Photoshop Lightroom (post processing software).

But post processing is a compromise between sharpness and noise. Go too far either way, and you will have less than acceptable results.

http://www.althephoto.com/concepts/iso.php

The referenced webpage shows the photos I took at that hockey game, and how noise looked, before and after fixing in photoshop. While the after photo was not quite as sharp, it was about the best I could do with the lens.

Photoshop Lightroom software costs between $150 and $300, depending if it is on sale (which happens several times a year).

Tamron 70-200 2.8, its more cheaper than the nikon 70-200 2.8 and almost have the same quality